Data-driven modeling of linear dynamical systems with quadratic output in the AAA framework

TL;DR

This paper extends the AAA algorithm to develop a data-driven modeling framework for linear systems with quadratic output, enabling efficient approximation of their transfer functions through interpolation and least-squares minimization.

Contribution

The paper introduces the AAA-LQO algorithm, combining barycentric representations and interpolation theory for quadratic output systems, a novel approach in data-driven modeling.

Findings

The AAA-LQO algorithm accurately models LQO systems from data.

Numerical tests demonstrate the efficiency of the proposed method.

The approach effectively interpolates transfer functions with minimal samples.

Abstract

We extend the AAA (Adaptive-Antoulas-Anderson) algorithm to develop a data-driven modeling framework for linear systems with quadratic output (LQO). Such systems are characterized by two transfer functions: one corresponding to the linear part of the output and another one to the quadratic part. We first establish the joint barycentric representations and the interpolation theory for the two transfer functions of LQO systems. This analysis leads to the proposed AAA-LQO algorithm. We show that by interpolating the transfer function values on a subset of samples together with imposing a least-squares minimization on the rest, we construct reliable data-driven LQO models. Two numerical test cases illustrate the efficiency of the proposed method.